One example could be when he tries to train with a new jutsu and fails miserably but still has a big smile on his face, determined to keep trying. In some fanfictions, he might be shown taking care of small animals in a really clumsy but sweet way. Another instance could be when he gives a handmade gift to his friends, like a poorly - drawn picture of them all together, which shows his innocent and cute side.
There are fanfictions where Naruto's innocence regarding love is shown. For instance, he might be completely clueless about the romantic feelings of a character towards him. He's so focused on his ninja training and his dreams that he doesn't pick up on the subtle cues. Also, in some stories set in alternate universes, Naruto's innocent view of the world is contrasted with the darker aspects of that new world, which emphasizes his innocence even more.
Well, there are quite a few examples. Some fanfic authors make Naruto so OP that he can resurrect the dead with ease. He may also have the power to absorb any jutsu used against him and then use it back at his opponents with double the power. In certain fanfictions, Naruto has an unbreakable shield made of pure chakra that can withstand any attack, no matter how powerful. These are all ways in which he is made overpowered in fan - created stories.
One great fanfiction could be 'Naruto's Adorable Adventures'. It might show Naruto in his daily life in Konoha, doing cute things like befriending little animals while on a mission or getting into harmless mischief with his friends. His innocent and positive attitude makes every situation he's in super cute.
In some fanfiction, there could be a situation where a new organization wants to use the Nine - Tails for their evil experiments. Naruto, being aware of this, would go on a solo mission to stop them. He would put himself in danger to ensure the Nine - Tails' safety. Also, if there were rumors or threats of someone trying to steal the Nine - Tails' power, Naruto would increase his guard and be extra vigilant, ready to defend at any moment.
In the fanfiction, Jiraiya often tells Naruto stories about his past adventures. These stories are not just for entertainment but also to teach Naruto about courage, perseverance, and the values of a ninja. For instance, the stories of Jiraiya's battles with powerful enemies show Naruto what it takes to be a strong and respected ninja. Jiraiya also protects Naruto when they are in dangerous situations, putting Naruto's safety above his own, which is a very fatherly thing to do.
One example could be a story where Naruto is in a dangerous mission and Gaara shows up unexpectedly to protect him. Gaara uses his sand powers to shield Naruto from enemy attacks, showing his loyalty and protectiveness.
One example could be a fanfic where during a battle in the Hidden Leaf Village, Naruto immediately stands in front of Hinata when an enemy attacks. He uses his shadow clone jutsu to surround her and keep her safe. His focus is solely on her protection, not even thinking about the battle strategy until he's sure she's out of harm's way.
A great fanfiction example could be set during a festival in the village. Hinata is excited to participate in a traditional dance, but Naruto is worried she might get hurt in the crowded area. So he stays really close to her, almost like a bodyguard. He scares off any guys who look at Hinata a bit too long. Another aspect could be in a training session where Hinata is paired with a tough opponent. Naruto is so overprotective that he tries to interfere in the training, thinking the opponent is being too rough. This causes some tension between Naruto and Hinata at first, but eventually they work it out and their relationship grows stronger.
One example could be a fanfiction where Naruto realizes his true feelings for Hinata and becomes confident in expressing his love. He might start by doing small things like bringing her flowers or asking her to train together more often. This new - found confidence could lead to a deeper connection between them as Hinata is pleasantly surprised by Naruto's actions.
I'm not sure of specific fanfictions where Naruto is an author off - hand. But it could be something like he writes a book about his battles against powerful foes, and it becomes a best - seller in the fanfiction's village. This book then might inspire other characters to train harder.